Q28 / 60 · KVPY 2012 (SA) · Mathematics
Two workers A and B are engaged to do a piece of work. Working alone, A takes 8 hours more to complete the work than if both worked together. On the other hand, working alone, B would need $4 \frac{1}{2}$ hours more to complete the work than if both worked together. How much time would they take to complete the job working together?
- A4 Hours
- B5 Hours
- Correct answerC6 Hours
- D7 Hours
Solution
If A \& B work together take time t hr. If A work alone takes $t+8 \mathrm{hr}$. to complete the work Work $/ \mathrm{hr}$ by $\mathrm{A}$ is $\frac{1}{\mathrm{t}+8}$. Similarly for B work/hr is $\frac{1}{\mathrm{t}+9 / 2}$
When A \& B work together there work/hr $\frac{1}{t+8}+\frac{1}{t+9 / 2}$
Work will be done in t hr.
$\mathrm{t}\left(\frac{1}{t+8}+\frac{1}{t+9 / 2}\right)=1$
By solving
$\mathrm{t}=6$
Hence, the correct answer is option: 'C'.